
\(U(x)=0\)  and \(W(x)=4x^2+w_0\)  or \(W(x)=8x^2+w_0\) , which are self-adjoint examples given in [1]}, with \(g=1\)  and \(g=2\)  respectively.

\(U(x)=\pm 4{\rm i}\)  and \(W(x)=4x^2+w_0\) , which is a non self-adjoint case, with \(g=1\) , see [2]}, [3]}.

\(U(x)=\pm 8{\rm i}\)  and \(W(x)=16x^2+w_0\) , which is a non self-adjoint case with \(g=2\) , as we will prove in Section REF , Example REF .

\(U(x)=\pm 12{\rm i}\)  and \(W(x)=12x^2+w_0\) , which is a non self-adjoint case, with \(g=2\)  as we will prove in Section REF , Example REF .

